Maximum Research Articles

X-vine models for multivariate extremes

Abstract Regular vine sequences permit the organization of variables in a random vector along a sequence of trees. Vine-based dependence models have become greatly popular as a way to combine arbitrary bivariate copulas into higher-dimensional ones, offering flexibility, parsimony, and tractability. In this project, we use regular vine sequences to decompose and construct the exponent measure density of a multivariate extreme value distribution, or, equivalently, the tail copula density. Although these densities pose theoretical challenges due to their infinite mass, their homogeneity property offers simplifications. The theory sheds new light on existing parametric families and facilitates the construction of new ones, called X-vines. Computations proceed via recursive formulas in terms of bivariate model components. We develop simulation algorithms for X-vine multivariate Pareto distributions as well as methods for parameter estimation and model selection on the basis of threshold exceedances. The methods are illustrated by Monte Carlo experiments and a case study on US flight delay data.

Applying a time-varying GEV distribution to correct bias in rainfall quantiles derived from regional climate models

Abstract Climate warming is causing an increase in extreme hydrometeorological events in most parts of the world. This phenomenon is expected to continue and will affect the frequency and intensity of extreme precipitation events. Although bias correction in regional climate model simulations has also been used to assess changes in precipitation extremes at daily and longer time steps, trends in the series predicted have seldom been considered. We present a novel bias correction technique that allows for the correcting of biases in the upper tails of the Generalized Extreme Value (GEV) distribution, while preserving the trend in projected precipitation extremes. The concept of non-stationary bias correction is demonstrated in a case study in which we used four EURO-CORDEX RCM models to estimate future rainfall quantiles. Historical observations have been used to correct biases in historical runs of the RCMs. The mean relative change in rainfall quantiles between the 1991–2021 historical period and the time horizon of 2080 was found to be 13.5% (st. dev.: 2.9%) for the return period of 2 years, which tends to decline with increasing return periods. Upon the return periods of 50 and 100 years, the mean relative change was predicted to be 5.5% (st. dev.: 1.1%) and 4.8% (st. dev.: 1%), respectively.

Applying clustered artificial neural networks to enhance contaminant diffusion prediction in geotechnical engineering

This paper introduces a novel approach using Clustered Artificial Neural Networks (CLANN) to address the challenge of developing predictive models for multimodal dataset with extreme parameter values. The CLANN method strategically decomposes the dataset, derived from Finite Element Analysis (FEA), into clusters, each representing distinct diffusion behaviors, and applies specialized neural networks within these clusters. The CLANN model was rigorously evaluated and demonstrated superior accuracy and consistency compared to traditional methods such as the Adaptive Neuro-Fuzzy Inference System (ANFIS) and fuzzy expert systems. While these conventional models struggled to capture the full range of diffusion dynamics, particularly under extreme conditions, CLANN consistently provided predictions that closely aligned with the actual FEA data across all scenarios. The versatility of the CLANN approach extends beyond its application to soil contamination. Its ability to handle complex, multimodal datasets suggests that this methodology can be generalized to a wide range of scientific and engineering problems characterized by similar data structures. This makes CLANN not only a powerful tool for geotechnical engineers but also a promising framework for broader applications where traditional models fall short. The findings of this study pave the way for more accurate, reliable, and adaptable predictive modeling in diverse domains, enhancing our ability to manage and mitigate environmental and engineering challenges.

Passage of Pi Since Antiquity Emphasizing Indian Evolution

This research article is an effort to explore the intriguing fact about the Indian evolution of mathematical constant π being ratio between circumference and diameter of any circle whose decimal part is never ending and non-repetitive having transcendental in nature. The Indian evolutionary passage started since ancient past Indus Civilization approximately during 3000 B.C, continued up to the great Ramanujan and still being worked on. Though, it has no constant value but it is an essential integral part in various branches of scientific occurrences and formulae used as constant. Its extreme utility value in daily life made it indispensible. Some examples of its daily uses are: a) Electricians apply it to solve various problems for electrical applications. b) Statisticians use it in track population dynamics c) Its medical benefits are to study the structures of eye d) Physicists uses it while calculating behavior of fluid ripples e) Biotechnologists use it to explain structure/function of DNA. f) It is also used in designing pendulum clocks. g) Aero designers use it to calculate outer surface area of aircraft. h) Used to calculate frequencies in waves used in signal processing (the period of sine waves is 2π. i) Used in GPS for navigation. j) In geometrical problems of circular and spherical designs where circumference of circle is 2πr, area π , volume of spherical structure = π , surface area of it is 4π . k) Used to get Wi-Fi to work on in jet planes through satellite communication system). l) It helps a controller, drive a motor to move an actuator, which controls the flaps on aircraft wings and tails in jet planes. The equation of angular frequency ω= 2πf radians; f= in Hz; where T is time. m) To assess vessels size at refineries, where volume of cylindrical vessels are governed by the formula 2πrh.

Assessment of Hoisting Conveyance Guiding Forces Based on Field Acceleration Measurements and Numerical Simulation

Shafts play a key role in the operation of mining plants. They connect underground excavations with the surface and provide the ability to transport people, equipment, and raw materials. The nature of the dynamic interaction of a conveyance moving at a significant speed along deformed guide rails is complex, and the method of assessing the interaction of hoisting conveyances with shaft steelwork, despite ongoing research, still requires further understanding and improvement. Misalignments of the guide rails and conveyance movements transverse to the shaft axis induce impact (guiding) forces, which are the key design parameters of shaft steelwork. The reliable assessment of guiding forces allows the design of safe and economical steelworks and the assessment of their structural safety during operation under deformations and corrosive deterioration. Determining the value of guiding forces requires their field measurements or the use of approximate empirical formulas. Both methods have their limitations—measurement is expensive and interferes with normal shaft operation, while empirical formulas are subject to high error due to the lack of consideration of many structural details specific to each shaft that significantly affect the behavior of the system. This study presents a new method for using a relatively simple-to-implement measurement of hoisting conveyance acceleration to assess guiding forces. A finite element model of the skip and steelwork was built, and simulations of the conveyance interaction with the structure were carried out. A strong relationship between the sliding plate’s impact point location and the guiding force was found. Extreme values of the guiding force were observed in the vicinity of the bunton connection. The study showed that reducing the skip load mass does not affect the force value. Simplified methods of calculating the moments of inertia of the hoisting conveyance significantly overestimate the code-based values of the guiding forces. The presented method considers the actual stiffness and mass distribution of hoisting conveyance and, therefore, allows for a more accurate estimation of the guiding forces and the transport of larger loads. This data-driven approach allows for the continuous monitoring of the guiding forces, the adjustments of the hoisting parameters, the rational planning of repairs, and a reduction in the replacement of corroded shaft steelwork.

Extreme rainfall in Dakar (Senegal): a case study for September 5, 2020

West African countries frequently experience extreme rainfall events during the monsoon season. On September 5, 2020, a significant event occurred in the Dakar region of Senegal with daily rainfall totals exceeding 90 mm, causing widespread flooding and displacing 1,000's of people. Despite the severity of this event, the physical mechanisms driving such extreme rainfall remain unexplored. This study aims to investigate the physical mechanisms associated with this event using multiple data sources, including satellite rainfall estimate products (GPM-IMERG, CHIRPS) and reanalysis data (ERA-5). By analyzing wind fields and mid-tropospheric moisture content from reanalysis data, we examined the synoptic-dynamic evolution of the atmosphere and the movement of the cyclonic vortex that transported moisture to the affected region, resulting in substantial rainfall measurements exceeding 100 mm. The analysis also revealed that a vortex over the ocean slowed down the vortex near Senegal, prolonging the rainfall over a total period of 10 h. Additionally, this study presents a comprehensive comparative analysis of state-of-the-art satellite rainfall estimates, assessing their accuracy and reliability in capturing extreme rainfall events both spatially and at specific rainfall gauges situated in Dakar. This evaluation revealed that while satellite rainfall estimates are valuable, they tended to underestimate (up to 40%) the actual rainfall observed at the Dakar-Yoff station. Furthermore, extreme value analysis showed that there is a tendency to underestimate return levels for high-intensity events, with some cases showing underestimations by up to twice the actual values. Thus, this research advances our understanding of extreme rainfall events in West Africa and improves our knowledge of satellite-based rainfall estimates, contributing to future monitoring and preparedness. Furthermore, these findings highlight the importance of monitoring cyclonic systems associated with African Easterly Waves, contributing to a better understanding of extreme rainfall events in West Africa.

Localization of Turn Points in the Rhythmic Movement of Sound Image

The localization of start and turn points in rhythmic sound movement created through the modeling of binaural beats (BB) was investigated. The BB-modeled broadband stimuli consisted of stationary initial and final segments with a section of cyclic motion between them. Spatial effects were induced by changes in the interaural time difference (ITD). During the experiment, subjects assessed the position of the movement trajectory ends or the position of reference points using a graphic tablet. It was discovered that the perception of rhythmic movement of the sound image was significantly influenced by the integrative ability of the binaural auditory system. The results indicated that with instantaneous switching between stationary segments, the perceived positions of the trajectory ends (start point and turn point) matched the positions of the reference points. Conversely, the smooth movement between the same extreme values showed a displacement of the trajectory ends: the turn points were localized further from the reference points compared to the start points, at all trajectory positions in space. Localization of the trajectory end crucially depended on the time that the sound had stayed near the turning point. These patterns were expressed stronger in the central area of the acoustic space compared to the periphery.

Fluvial Sediment Load Characteristics from the Yangtze River to the Sea During Severe Droughts

Most river deltas worldwide are located in well-developed, densely populated lowland regions that face challenges from accelerated sea level rise. Deltas with morphological equilibrium are the foundation for associated prosperous economies and societies, as well as for preserving ecological fragile environments. And for deltas to be in morphological equilibrium, sufficient fluvial sediment supplies are fundamental. Severe droughts have significant impacts on the sediment load discharged to the sea, but this is considerably less studied compared to flooding events. This study examines the characteristics of Yangtze River sediment flowing toward the East China Sea during severe droughts. The effect of the Three Gorges Dam (TGD) was investigated by comparing the difference before and after its construction in 2003. Results indicate that the sediment load from the Yangtze River to the sea has experienced a more pronounced decrease during severe drought years since 2003. The primary cause is a substantial reduction in sediment supply from the upper reaches, resulting from the impoundment of the Three Gorges Reservoir created in 2003 and the construction of additional major reservoirs in the upper reach thereafter. Simultaneously, this is accompanied by the fining of sediment grain size. The fining of sediment and considerably reduced sediment load discharged to the sea during severe droughts after 2003 are likely to accelerate the erosion of the Yangtze subaqueous delta. The rating parameter values during severe drought years fall within the range observed in normal years, indicating that these drought events do not align with extreme rating parameter values. Less than 30% of the average discrepancy between measured and reconstructed sediment loads in severe drought years before 2003, and approximately 10% of the discrepancy after 2003, demonstrate the feasibility of reconstructing sediment loads for severe drought events using a sediment rating curve. This rating curve is based on daily water discharge and sediment concentration data collected during the corresponding period. These findings indicate that the rating curve-based reconstruction of sediment load performs well during severe droughts, with relative error slightly exceeding the average error of normal years prior to 2003 and approaching that observed after 2003. This study provides insights on sediment management of the Yangtze River system, including its coastal zone, and is valuable for many other large river systems worldwide.

Optimal attention allocation: picking alpha or betting on beta?

We investigate a problem of attention allocation and portfolio selection with information capacity constraint and return predictability in a multi-asset framework. In a two-phase formulation, the optimal attention strategy maximizes the combined expected alpha payoffs and expected beta payoffs of the portfolio. Return predictors taking extreme values incentivize the investor to learn about them and this leads to competition among information sources for attention. Moreover, the investor trades with varying skills including picking alphas and betting on beta, depending on the magnitude of the related predictors. Our multi-period analysis using reinforcement learning demonstrates time-horizon effects on attention and investment strategies.

Estimation and Inference for Extreme Continuous Treatment Effects*

This paper studies estimation and inference for the treatment effect in deep tails of the potential outcome distributions corresponding to a continuously valued treatment, namely the extreme continuous treatment effect. We consider two measures for the tail characteristics: the quantile function and the tail mean function defined as the conditional mean beyond a quantile level. Then, for a quantile level close to 1, we define the extreme quantile treatment effect (EQTE) and extreme average treatment effect (EATE), which are, respectively, the ratios of the quantile and tail mean at different treatment statuses. We propose estimators for the EQTE and EATE based on tail approximations from the extreme value theory. Our limiting theory is for the EQTE and EATE processes indexed by a set of quantile levels and pairs of different treatment statuses. It facilitates uniform inference for the EQTE and EATE over multiple tail levels and multiple treatment effects. Simulations suggest that our method works well in finite samples, and an empirical study illustrates its practical merits.

Origins of Extreme CAPE Around the World

AbstractSevere convection, responsible for hazards such as tornadoes, flash floods, and hail, is usually preceded by abundant convective available potential energy (CAPE). In this work, we use a Lagrangian approach to study the buildup of anomalously large values of CAPE from 2012 to 2013 in various regions. Nearly all extreme values of CAPE arise from surface fluxes underneath a layer of convective inhibition (the CIN layer) over several diurnal cycles, but the origin of the CIN layer and the diurnal cycle of surface fluxes differ around the world. In some regions, such as North America and Europe, the air above the boundary layer must be much warmer than usual to form this CIN layer, whereas in other regions, especially the Middle East and central Africa, a CIN layer is common. Additionally, high CAPE occurrences that are over land (those in the Americas, Europe, Africa, and Southeast Asia) tend to lose their CIN layers before the time of maximum CAPE due to large diurnal cycles of sensible heating, whereas those that occur over coastal waters (in the Middle East, Northern Australia, South Asia, and the Mediterranean) usually retain substantial convective inhibition. Uniquely, CAPE in Southeast Australia often builds up due to cooling aloft rather than to boundary layer warming. These results show that one hoping to understand or predict CAPE patterns must understand a variety of mechanisms acting in different regions.

Wall temperature effects in high-enthalpy supersonic turbulent channel flows considering air dissociation

Direct numerical simulations of temporally evolving high-enthalpy supersonic turbulent channel flows are performed at a Mach number of 3.0 and Reynolds number of 4880. The high-enthalpy air is assumed to behave as a chemical and thermal equilibrium of five-species mixture. The wall temperatures in the range of 1733.2 K to 4100.0 K to study the influence of wall temperature on the chemical activity, turbulent statistics and aerodynamic characteristics. The results show that the chemical activity is remarkable because the air is relatively sufficient dissociated. When the wall temperature higher than 2300 K, an extreme value can be observed in the distributions of mean and fluctuating mass fraction of atomic nitrogen close to the wall. Many of the influence of wall temperature on the turbulent statistics which hold for low-enthalpy conditions also hold for high-enthalpy conditions, including mean and fluctuating velocity, recovery enthalpy, and strong Reynolds analogy. As the wall temperature increases, the turbulent momentum flux and turbulent heat flux decrease, the turbulent mass flux mainly depends on species mass fractions fluctuations. The integral formulas of decomposing the aerodynamic characteristics are proposed, and the predicted heat flux and skin friction are all in good agreement with those direct estimation. The wall temperature does not change the primarily contributions of aerodynamic characteristics. Although the turbulent heat flux term is approximately 6%, its part of turbulent transport of enthalpy significantly increases with increasing wall temperature. The turbulent Schmidt number is insensitive to wall temperature.

Analysis of the heterogeinety impact of oil prices shocks on exchange rates in oil exporting countries: evidence of quantiles-on -quantiles approach

The objective of this study is to investigate the heterogeneous dynamic between exchange rate returns and oil prices in oil exporting countries. Precisely, the researchers used the exchange rates returns of both low incomes, emerging and developed majors oil exporting countries, and decomposed oil price shocks to study the heterogeneity of the intrinsic dynamic between the two variables in these countries, using the quantile-on-quantile analysis. The findings revealed that, although the dynamic between oil prices shocks and exchange rates returns is largely negative in these countries, there are important variability of the shocks impacts across the quantile distribution of both exchange rates returns and the different oil price shocks. More precisely , the study reavealed the heterogeneity of the different oil shocks impacts (oil aggregate demand , oil supply and oil specific demand shocks) on the exchange rates return of a given country , with the shape of the QQR graphs being different according to the source of shock and the magnitude of oil demand and oil specific demand shocks being more significant than that of oil supply shocks in many of the cases. In the same way , the analysis results also indicate that the dynamic between oil price shocks and exchange rate is heterogenous across the countries , with the impact of the shocks being more significant in developing countries than it is in developed countries . As well the behavior of the exchange rates returns at extreme values is different from one country to another. From this insight, the researcher recommends an economy diversification mainly for oil developing countries, and country-specific economy policies to mitigate the incidence of oil shocks, as the impact differs from one country to another.. Keywords: Exchange Rates, Oil Prices, Quantile-on-Quantile, Oil Exporting Countries.

Maximum non-bounded difference method for overbounding Global Navigation Satellite System errors

Global Navigation Satellite Systems (GNSS) support numerous applications, including mission-critical ones that require high integrity for safe operations such as air, maritime, and land-based navigation. These applications require ensuring the upper bound of the positioning computation, including overbounding any assumptions made in positioning algorithms. One of the main assumptions in the GNSS positioning algorithm is that the error follows a Probability Density Function (PDF), widely assumed to be Gaussian. This assumption should be overbounded to ensure safety. Two mathematical definitions of distribution overbounding have been proposed: Cumulative Distribution Function (CDF) overbounding and paired overbounding. Achieving these definitions has been an open problem for the past 20 years, and to date, no methods have effectively achieved either definition in multimode datasets. This paper proposes the first overbounding method, the Maximum non-Bounded Difference (MnBD) method, capable of achieving both definitions. Its effectiveness is assessed by comparison with the combined CDF bounding and paired overbounding approach. The results show that the MnBD method successfully achieves overbounding in both real datasets and 1000 simulated multimode data, tested on Gaussian and Generalized Extreme Value (GEV) distributions. The latter demonstrates MnBD’s ability to handle asymmetric distributions. The developed approach can be utilized in overbounding the GNSS error at the system level and user level to ensure the system integrity.

Natural assets, changes, and variations of the socioeconomic-environmental systems along the Asian drylands belt

Abstract The amount of and changes in a country's natural assets are crucial for developing national strategic plans and policies due to their foundational role in determining the resilience of social-environmental systems (SES), especially under a changing climate. Many integrated metrics on natural assets have been proposed based on individual measures to provide insights into the state of national natural resources. This is particularly true for countries experiencing extreme environmental stresses. Drawing on longitudinal data spanning from 1980 to 2020, the objective of this study is to analyze nuanced distinctions across 23 political entities (PEs) in the dryland regions of mid-latitudinal Asia, investigating their interannual variabilities over the four-decade study period and discerning potential driving forces. We examined three key integrated measures of the SES: ecosystem water use efficiency (WUE), human appropriation of net primary production (HANPP), and human appropriation of water resources (HAWR). We found increased variability as well as spikes in extreme values in each of these three measures of SES function among the 23 PEs over the study period. Water stress played an increasing and more important role than temperature in influencing the magnitude and variations of the three measures. Our results also indicate that human interventions may help increase the efficiency of water use in this dryland region of the world.

Extreme Precipitation Events During the Wet Season of the South America Monsoon: A Historical Analysis over Three Major Brazilian Watersheds

Most of South America, particularly the region between the southern Amazon and southeastern Brazil, as well as a large part of the La Plata Basin, has its climate regulated by the South American Monsoon System. Extreme weather and climate events in these areas have significant socioeconomic impacts. The Madeira, São Francisco, and Paraná river basins, three major watersheds in Brazil, are especially vulnerable to wet and drought periods due to their importance as freshwater ecosystems and sources of water for consumption, energy generation, and agriculture. The scarcity of surface meteorological stations in these basins makes meteorological studies challenging, often using reanalysis and satellite data. This study aims to identify extreme weather (wet) and climate (wet and drought) events during the extended wet season (October to March) from 1980 to 2022 and evaluate the performance of two gridded datasets (CPC and ERA5) to determine which best captures the observed patterns in the Madeira, São Francisco, and Paraná river basins. Wet weather events were identified using the 95th percentile, and wet and drought periods were identified using the Standardized Precipitation Index (SPI) on a 6-month scale. In general, CPC data showed slightly superior performance compared to ERA5 in reproducing statistical measures. For extreme day precipitation, both datasets captured the time series pattern, but CPC better reproduced extreme values and trends. The results also indicate a decrease in wet periods and an increase in drought events. Both datasets performed well, showing they can be used in the absence of station data.

Dual Power Transformation and Yeo–Johnson Techniques for Static and Dynamic Reliability Assessments

This paper addresses key challenges in the static and dynamic reliability analysis of engineering structures, particularly the difficulty in accurately estimating large reliability indices and small failure probabilities. For static reliability problems, a dual power transformation is employed to transform the performance function into a form approaching a normal distribution. The high-order unscented transformation is then applied to compute the first four moments of the transformed performance function. Subsequently, the fourth-moment method is used to calculate large reliability indices, offering a novel improvement over traditional methods such as FORM and SORM. For dynamic reliability problems, the low-discrepancy sampling technique is integrated to efficiently compute structural responses under random seismic excitation, improving computational efficiency for complex dynamic systems. The Yeo–Johnson transformation is introduced to normalize the extreme values of dynamic responses, and the first four moments of the transformed extreme values are statistically evaluated. Additionally, a third-order polynomial transformation (TPT) is applied to approximate the probability density function, leading to the derivation of the probability of exceedance (POE) curve. The optimal transformation parameters for both the dual power and Yeo–Johnson transformations are determined using the Jarque–Bera (JB) test. Four numerical examples, coupled with Monte Carlo simulation, validate the proposed framework’s accuracy and efficiency, providing a robust tool for static and dynamic reliability analysis. This unified approach represents a significant advancement by integrating novel transformations and fourth-moment method, providing a powerful and efficient tool for static and dynamic reliability analysis of engineering structures.

Comparison between a priori and a posteriori slope limiters for high-order finite volume schemes

High-order finite volume and finite element methods offer impressive accuracy and cost efficiency when solving hyperbolic conservation laws with smooth solutions. However, if the solution contains discontinuities, these high-order methods can introduce unphysical oscillations and severe overshoots/undershoots. Slope limiters are an effective remedy, combating these oscillations by preserving monotonicity. Some limiters can even maintain a strict maximum principle in the numerical solution. They can be classified into one of two categories: a priori and a posteriori limiters. The former revises the high-order solution based only on data at the current time tn, while the latter involves computing a candidate solution at tn+1 and iteratively recomputing it until some conditions are satisfied. These two limiting paradigms are available for both finite volume and finite element methods.In this work, we develop a methodology to compare a priori and a posteriori limiters for finite volume solvers at arbitrarily high order. We select the maximum principle preserving scheme presented in [1,2] as our a priori limited scheme. For a posteriori limiting, we adopt the methodology presented in [3] and search for so-called troubled cells in the candidate solution. We revise these cells using a robust MUSCL fallback scheme, diverging from the traditional Multi-dimensional Optimal Order Detection (MOOD) framework by allowing each candidate solution to undergo only a single revision. This modification enables our a posteriori schemes to achieve competitive computational speed while permitting small, though non-zero, maximum principle violations.The linear advection equation is solved in both one and two dimensions and we compare variations of these limited schemes based on their ability to maintain a maximum principle, solution quality over long time integration and computational cost.This analysis reveals a fundamental tradeoff between these three aspects. The high-order a posteriori limited solutions boast excellent quality at long time-scales, taking full advantage of the sharp gradients of the high-order finite volume method. However, their relaxed implementation allows for consistent, albeit small, violations of the maximum principle. In contrast, high-order a priori limited solutions rigorously uphold the maximum principle but suffer from numerical artifacts and diffusion that increasingly dominate at extended time scales. The convex blending of revised fluxes can mitigate the maximum principle violations in a posteriori schemes but introduces more noticeable numerical artifacts. These results suggest a fundamental trade-off between robustness against numerical diffusion and the preservation of a strict maximum principle.Moreover, we compare two methods for computing the flux integrals along two-dimensional cell faces, revealing that one option is more cost-effective but leads to particularly large violations when used with the a priori limited scheme. Consequently, the a priori limited scheme is forced to use the more costly flux computation, making it significantly more expensive at higher-order than the a posteriori limited scheme on CPU architecture. This cost difference can be almost entirely mitigated using a GPU implementation of the same schemes, highlighting that GPUs are well-suited for high-order finite volume stencil operations.

Deflection characteristics of semi-rigid base asphalt pavement under traffic speed deflectometer loading

The three-dimensional viscoelastic finite element simulation and on-site validation was combined, so as to study the characteristics of the traffic speed deflection slope curve of the semi-rigid base asphalt pavement. Results show that there is an inert point in the deflection slope curve when only the surface or base structural state changes. With the loading center approaching transverse crack, the ‘three extreme values’ attribute transitions gradually to ‘single extreme value’. For the surface-base penetrating longitudinal crack caused by uneven subgrade settlement, the peak value of deflection slope curve increases significantly as the crack approaches the loading center, reaching an order of magnitude difference, and the attribute transforms from ‘three extreme values’ to ‘single extreme value’. Indicators characterizing the layered structural state were proposed, and the indicator change rules and applicability for the pavement with different surface and base layer thicknesses, under different deflectometer speeds, with or without cracks, were discussed.

Exploring the Impact of Trade Credit and Debt on Systemic Risk in the Presence of Financial Distress and Constraints

Based on the extreme value and network contagion theories, this study intends to explore the effects of trade credit, and short/long-term debt on the systemic risk of 205 Pakistani non-financial firms over the period from 2005 to 2021. To evaluate the firms’ systemic contribution and vulnerability, we apply two firm-specific measures, the change in conditional value-at-risk (DCOVAR) and marginal expected shortfall (MES). Our findings reveal a significantly positive impact of trade credit, and short/long-term debt on the systemic contribution and vulnerability of these firms. The findings also indicate that the underlying relationship is significantly moderated by financial distress and financial constraints. Understanding how different forms of debt influence systemic risk can guide policymakers in crafting regulations or interventions to promote a healthier financial environment. Regulators may reevaluate the balance between short/long-term debt usages or develop guidelines for managing trade credit effectively to mitigate systemic risk.